1. Field of the Invention
The present invention relates to a method of measuring a three-dimensional posture of a sphere, a method of measuring a rotational amount and a direction of the rotational axis of the sphere, and an apparatus of measuring the three-dimensional posture of the sphere. More particularly the present invention relates to a method of measuring the posture of the sphere such as a golf ball, a baseball ball, a tennis ball, and the like and its rotational amount.
2. Description of the Related Art
Various methods and apparatuses of measuring the rotational amount and the like of the sphere such as a golf ball are known.
According to a known method, light is emitted to a sphere having a reflection tape bonded to its surface or to a sphere having a region, painted in black on its surface, not reflecting light therefrom. The rotational amount of the sphere is measured from change in the amount of reflection light obtained by the rotation of the sphere. However according to this method, because only the optical amount is measured but the contour of the sphere and the displacement of its posture are not measured, it is impossible to specify the direction of the sphere. Thus normally, the rotational amount of the sphere and the direction of its rotational axis are found from a displacement situation of marks of each of a plurality of images of a sphere photographed at predetermined intervals when the sphere is flying in rotation.
As apparatuses and methods of finding the rotational amount of the sphere from images of a photographed mark-given sphere, the following measuring apparatuses and methods are known: The apparatus for measuring the rotational amount of the sphere disclosed in U.S. Pat. No. 2,810,320, the method of measuring the motion of a golf ball disclosed in Japanese Patent Application Laid-Open No. 10-186474, and the apparatus for measuring the flight characteristic of sporting goods disclosed in U.S. Pat. No. 2,950,450.
In the measuring apparatus disclosed in U.S. Pat. No. 2,810,320, as shown in FIGS. 16A and 16B, the sphere T, having the center C, to which the marks P and Q are given is photographed twice to obtain two two-dimensional images G1 and G2, and the radius of the sphere in each of the two-dimensional images G1 and G2 is specified as the unit radius. Further the three-dimensional coordinate of each of the marks P and Q and the center C is computed from the two-dimensional coordinate on the two-dimensional image G1. The three-dimensional coordinate of each of the marks P′ and Q′ and the center C′ is also computed from the two-dimensional coordinate on the two-dimensional image G2. These computed three-dimensional coordinates are set as three-dimensional vectors to find the vector movement amount between the two images G1 and G2 to thereby compute the rotational amount of the sphere T and the direction of its rotational axis.
With reference to FIGS. 17A and 17B, in the measuring method disclosed in Japanese Patent Application Laid-Open No. 10-186474, the ball image G3 having the two balls B1 and B1′ photographed thereon is obtained by photographing the ball B1 with the first and second cameras 1A and 1B at an interval determined by the sensor 2 which detects the motion of a club when it hits the ball B1. The two-dimensional ball image G3 is processed by the method similar to that of the measuring apparatus disclosed in U.S. Pat. No. 2,810,320 to compute the rotational amount and the direction of its rotational axis.
With reference to FIGS. 18A and 18B, in the measuring apparatus 4 disclosed in U.S. Pat. No. 2,950,450, the balls B2 and B2′ to which the mark Ba has been given are photographed with the synchronized cameras 5A and 5B to obtain the images of the balls B2 and B2′. Based on the obtained images, the three-dimensional coordinate of the mark Ba is obtained based on the principle similar to the triangulation by relating the principle to the relationship between the visual field of the camera 5A and that of the camera 5B. Based on the obtained three-dimensional coordinate of the mark Ba, as shown in FIG. 18B, a view of the three-dimensional region of the balls B2 and B2′ is obtained to measure the characteristics of the balls B2 and B2′. The method of obtaining the three-dimensional coordinate in this manner is known as DLT (Direct Liner Transformation).
In addition to the above-described apparatuses and method, the apparatus 6 for detecting the posture of a three-dimensional object is disclosed in Japanese Patent Application Laid-Open No. 7-302341, as shown in FIG. 19. The posture detection apparatus 6 measures not the posture of a sphere, but the posture of the three-dimensional object by using a Genetic Algorithms. That is, a fitness value is found by comparing a plurality of images of the three-dimensional object 8 photographed with a plurality of cameras 7a–7n with a plurality of imaginary images of the imaginary three-dimensional object 9 formed in correspondence to the three-dimensional object 8. Based on the Genetic Algorithms conforming to the fitness value, the posture of the three-dimensional object 8 is detected by changing the posture of the imaginary three-dimensional object 9.
In the measuring apparatus shown in FIGS. 16A and 16B and the measuring method shown in FIGS. 17A and 17B, because the radius of the ball image is used in the computation for measurement, the accuracy of the three-dimensional vector which is computed depends on the accuracy of the radii of the sphere obtained from the images. Thus it is necessary to highly accurately photograph the ball images and find the radius of the sphere with high accuracy from the photographed images. To obtain a still image of the ball flying at a high speed, it is necessary to use a high-speed camera having a high-speed shutter. However because the high-speed shutter opens in a very short period of time, it is difficult to obtain a sufficient amount of light.
Therefore the photographed ball image is comparatively clear in the vicinity of the center of the ball, because the center of the ball confronts the camera. On the other hand, it is difficult to capture the contour of the ball clearly. Even though the manner of emitting the ball is adjusted, it is difficult to solve this problem. Consequently the contour of the photographed image of the ball is unclear. Thus the radius of the ball is read with low accuracy from the ball image, which causes the rotational amount of the ball and the direction of its rotational axis to be measured with low accuracy.
In the measuring apparatus shown in FIGS. 18A and 18B, the three-dimensional coordinate of the mark given to the surface of the ball is obtained not by using the radius of the ball image but on the basis of the length of an actual space. Thus it is unnecessary to photograph the contour of the ball clearly and the problem of shortage of luminous intensity rarely occurs, therefore a camera is required a low extent. However to find the three-dimensional coordinate of the mark given to the surface of the ball with high accuracy, it is necessary to photograph the ball in a comparatively large size to allow each mark to be read accurately. To photograph the ball in a large size, it is necessary to shorten the interval between two ball image-photographing times, which reduces the rotational amount of one ball image with respect to that of the other ball image.
To measure the rotational amount of the ball with high accuracy, it is necessary to increase the moving distance of the mark to thereby increase the displacement of the position of the mark, i.e., increase the amount of rotation of one ball image with respect to that of the other ball image, which necessitates a condition reciprocal to the increase of the ball image.
Thus it is possible to measure the three-dimensional coordinate of the mark with high accuracy by increasing the ball image. However, because the change of the positions between both images is small, the rotational amount of the ball cannot be measured with high accuracy. In the case where the ball is photographed in such a way as to increase the rotational amount of one ball image with respect to that of the other ball image, it is necessary to photograph the ball at a long interval. In this case, although the rotational amount of the ball can be measured with high accuracy, the ball images are small. Therefore the three-dimensional coordinate of the mark is measured with low accuracy. Thus the measuring apparatus is incapable of measuring both the three-dimensional coordinate of the mark and the rotational amount of the ball with high accuracy.
To solve the above-described problem, it is conceivable to prepare two sets of measuring apparatuses, obtain the image of one ball with a first measuring apparatus and the image of the other ball with a second measuring apparatus to measure both the three-dimensional coordinate of each mark and the rotational amount of each ball with high accuracy. However in measuring the three-dimensional coordinate of the mark and the rotational amount of the ball, it is necessary to make a calibration by associating the operation of four cameras of both sets of the measuring apparatuses with each other. Furthermore the measuring apparatus is required to have a very complicated construction and is hence expensive. As such, it is difficult to use two sets of the measuring apparatuses.
Further in computing the rotational amount of the ball from the movement amount of the photographed mark given to the surface of the ball, it is necessary to recognize the mark on the second ball image corresponding to the mark on the first ball image. However in the case where the direction of the rotational axis of the ball can be estimated and the change of the rotational amount of one ball image with respect to that of the other ball image is small, it is comparatively easy to recognize the mark on the second ball image corresponding to the mark on the first ball image. However in the case where the direction of the rotational axis of the ball cannot be estimated because the direction of the rotational axis of the ball changes greatly in each measurement or in the case where the rotational amount of the ball is large, it is very difficult to recognize the mark on the second ball image corresponding to the mark on the first ball image. In this case, there is a possibility that it is impossible to measure the rotational amount of the ball and the like by an automatic recognition program of a computer. In the case where a man recognizes the mark on the second ball image corresponding to the mark on the first ball image, it takes much time and may make an erroneous recognition of the mark.
In addition, it is impossible to make measurement in the case where the mark photographed on the first ball image moves to the reverse side of the ball owing to its rotation and does not appear on the surface of the ball image. In his case, there is a limitation in the measuring direction of the camera and the rotational direction of the ball. Thus the measuring apparatus has a problem that measurement cannot be accomplished in an optimum situation.
In the posture detection apparatus 6 shown in FIG. 19, since a plurality of cameras 7a–7n are used, the measuring cost is high. The ball is symmetrical with respect to the axis passing through its center. Thus when the posture of the ball, namely, the direction thereof changes, there is no change among the photographed images of the ball. That is, when the ball images and the imaginary images are compared with each other, the posture of the ball cannot be specified. Further in the posture detection apparatus 6, the fitness value is determined on the basis of an overlapping degree of a plurality of images. Thus it is necessary to photograph the ball image clearly. However in the case where the posture of the sphere such as the golf ball which moves at a high speed is measured, it is difficult for the cameras 7a–7n to follow and photograph the sphere moving at a high speed. It is almost impossible to take a photograph of the ball in such a way that all the images of the ball are clear. Because the fitness value is determined on the basis of the images containing a considerable degree of errors respectively, the posture detection apparatus 6 is incapable of measuring the posture of the ball with high accuracy.